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On a Direct Mercator chart at latitude 15°S, a certain length represents a distance of 120 NM on the Earth.The same length on the chart will represent on the Earth, at latitude 10°N, a distance of..
  • A
    117.7 NM.
  • B
    122.3 NM.
  • C
    118.2 NM.
  • D
    124.2 NM.

Charts represent the “reduced earth”.

The chart scale represents the relation between the length represented on the chart compared with the real distance on planet earth.

Chart Scale = Chart length / Earth distance

On a Mercator chart, scale expands away from the Equator. The scale expansion is proportional to the secant of the latitude.

Questions about scale in a Mercator chart, come in 1 of 4 basic types:

  • Given scale at the Equator, find Mercator scale at some other latitude.

  • Given Mercator scale at some latitude, find scale at the Equator.

  • Given Mercator scale at some latitude, find Mercator scale at some other latitude.

  • Given a fixed chart distance between meridians, find Mercator scale at a specific latitude.

The equation to remember to solve this questions is the following one:

Scale denominator A x cos (Latitude B) = Scale denominator B x cos (Latitude A)

You could use this formula, but you would come that the relation between the distances and the scale is a constant.
Manipulating the formula we came out with this:

Departure at A x cos (Latitude B) = Departure at B x cos (Latitude A)

Departure at B = 120 x cos (10º) / cos (15º) = 122,3 nm

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